INFINITARY TABLEAU FOR SEMANTIC TRUTH

We provide infinitary proof theories for three common semantic theories of truth: strong Kleene, van Fraassen supervaluation and Cantini supervaluation. The value of these systems is that they provide an easy method of proving simple facts about semantic theories. Moreover we shall show that they also give us a simpler understanding of the computational complexity of these definitions and provide a direct proof that the closure ordinal for Kripke's definition is omega(CK)(1). This work can be understood as an effort to provide a proof-theoretic counterpart to Welch's game-theoretic (Welch, 2009).